A comparison of confidence interval methods for the intraclass correlation coefficient in community-based cluster randomization trials with a binary outcome
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Bibliographic record
Abstract
BACKGROUND: Many investigators rely on previously published point estimates of the intraclass correlation coefficient rather than on their associated confidence intervals to determine the required size of a newly planned cluster randomized trial. Although confidence interval methods for the intraclass correlation coefficient that can be applied to community-based trials have been developed for a continuous outcome variable, fewer methods exist for a binary outcome variable. The aim of this study is to evaluate confidence interval methods for the intraclass correlation coefficient applied to binary outcomes in community intervention trials enrolling a small number of large clusters. Existing methods for confidence interval construction are examined and compared to a new ad hoc approach based on dividing clusters into a large number of smaller sub-clusters and subsequently applying existing methods to the resulting data. METHODS: Monte Carlo simulation is used to assess the width and coverage of confidence intervals for the intraclass correlation coefficient based on Smith's large sample approximation of the standard error of the one-way analysis of variance estimator, an inverted modified Wald test for the Fleiss-Cuzick estimator, and intervals constructed using a bootstrap-t applied to a variance-stabilizing transformation of the intraclass correlation coefficient estimate. In addition, a new approach is applied in which clusters are randomly divided into a large number of smaller sub-clusters with the same methods applied to these data (with the exception of the bootstrap-t interval, which assumes large cluster sizes). These methods are also applied to a cluster randomized trial on adolescent tobacco use for illustration. RESULTS: When applied to a binary outcome variable in a small number of large clusters, existing confidence interval methods for the intraclass correlation coefficient provide poor coverage. However, confidence intervals constructed using the new approach combined with Smith's method provide nominal or close to nominal coverage when the intraclass correlation coefficient is small (<0.05), as is the case in most community intervention trials. CONCLUSION: This study concludes that when a binary outcome variable is measured in a small number of large clusters, confidence intervals for the intraclass correlation coefficient may be constructed by dividing existing clusters into sub-clusters (e.g. groups of 5) and using Smith's method. The resulting confidence intervals provide nominal or close to nominal coverage across a wide range of parameters when the intraclass correlation coefficient is small (<0.05). Application of this method should provide investigators with a better understanding of the uncertainty associated with a point estimator of the intraclass correlation coefficient used for determining the sample size needed for a newly designed community-based trial.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.219 | 0.482 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.003 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it